How did the United States use the changing relationship between China and the Soviet Union to its own advantage?

The U.S. was quick to use worsening relations between the
Soviets and China to its advantage. This event, known as the Sino-Soviet Split, led
directly to the rapprochement of Chinese and American relations in the
1970’s.

China and the Soviet Union began to have a falling
out as early as the 1930’s when the Soviet Union backed Chang Kai Shek rather than Mao
Zedong during the Chinese Civil War. Although they appeared to become allies after World
War II, the rifts began to show as ideological difference formed between the two
communist countries. China wanted to continue aggressive action towards the west, which
the Soviets wanted to try and pursue peace. Soon, border clashes between the two sides
began to occur as well as full-blown criticism published in the international
press.

Nuclear war was barely averted in 1968, but this
event caused China to rethink its geopolitical strategy. They began to tone down their
anti-U.S. rhetoric and sought to lessen tensions between themselves and other western
superpowers. Seeing their Soviet neighbors as the greater threat, the Chinese extended
diplomatic invitations to the U.S. in 1972 and reopened trade relations and
international cooperation by hosting president Nixon. 

The
U.S. were more than happy to help drive a wedge between the two communist superpowers,
which they viewed as allies until the border clashes. Soon, the Soviets and China were
backing different political parties in a number of civil wars in African and the Middle
East while the U.S. gleefully played them off each other while the Vietnam conflict
wound down.